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@ARTICLE{,
    author = {Dostal{\'{\i}}k, Mark and Matyska, Ctirad and Prů{\v s}a, V{\'{\i}}t},
  keywords = {Extended boussinesq approximation, Thermal convection, Weakly nonlinear analysis},
     title = {Weakly nonlinear analysis of Rayleigh–B{\'{e}}nard convection problem in extended Boussinesq approximation},
   journal = {Applied Mathematics and Computation},
    volume = {408},
      year = {2021},
     pages = {126374},
      issn = {0096-3003},
       url = {https://www.sciencedirect.com/science/article/pii/S009630032100463X},
       doi = {10.1016/j.amc.2021.126374},
  abstract = {We investigate Rayleigh–B{\'{e}}nard convection problem in an extended Boussinesq approximation suitable for conditions in the Earths mantle. The aim is to evaluate the influence of depth-dependent material parameters, dissipation, adiabatic heating/cooling and heat sources on qualitative characteristics of thermal convection. We identify the critical values of dimensionless parameters that determine the onset of convection, and we characterize the dominating convection patterns in marginally supercritical states. These issues are addressed by the application of linear stability analysis and weakly nonlinear analysis. We have found that the character of convection differs substantially from the standard case of Rayleigh–B{\'{e}}nard convection.}
}